Over the next few days, the European Commission will draw up proposals to lift the sanctions.
The European Union has started to look at ways of ending its sanctions against Yugoslavia, but the announcement of a run-off in the presidential elections could delay any concrete decisions.
European Commissioner for External Affairs Chris Patten said that the EU would take into account events in Yugsolavia before deciding which sanctions could be lifted most rapidly.
France, which holds the rotating presidency of the EU, has called for a revision of the sanctions policy in view of the apparent success at the polls of the Serbian opposition.
Over the next few days, the European Commission will draw up proposals to lift the sanctions.
But a final decison is unlikely to be taken while President Slobodan Milosevic remains in office.
Mr Patten said that Mr Milosevic had been clearly rejected by the people of Serbia.
He said he hoped the question of Mr Milosevic's political survival would not arise, while adding that the EU would now look at the run-off announcement.
Uncertainty in Belgrade could delay any decisions.
French Foreign Minister Hubert Vedrine said Europe must respond to the courage of the Serbian people by fulfilling the promises it made should democracy prevail.
EU promise
On the eve of the elections, the EU had promised to lift all sanctions if the Serbian people rejected Mr Milosevic's policies.
The sanctions - imposed last year during the Serb crackdown in Kosovo - include an oil embargo, a freeze of Yugoslav assets abroad and a visa ban for hundreds of officials and businessmen associated with Mr Milosevic.
That may be the last to go, since each name on the list will have to be checked again.
But EU officials say that the other sanctions could be lifted in a matter of days or weeks, depending on when democracy takes hold in Serbia.